Question

Raportul dintre media aritmetica a 3 numere consecutive si suma patratelor lor este 1/7.Sa se afle nr.

Answer 1

( 3 x a + 3 ) / 3 → media aritmetica a 3 numere consecutive

= 3 ( a + 1 ) / 3 = a + 1

a² + ( a + 1)² + ( a + 2) ² = a² + a² + 2 a + 1 + a² + 4 a + 4 = 3 a² + 6 a + 5 → suma patratelor celor 3 numere consecutive

( a + 1 ) / ( 3 a ² + 6 a + 5 ) = 1 / 7

3 a² + 6 a + 5 = 7 a + 7

3 a² + 6 a - 7 a + 5 - 7 = 0

3 a² - a - 2 = 0

Δ = 1 + 24 = 25

a₁ = ( 1 + √25 ) / 6 = 6 / 6 = 1 ∈ N

a₂ = ( 1 - 5 ) / 6 = - 4/ 6 = - 2 / 3

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Numerele sunt: 1; 2 si 3

Verific: ( 1 + 2 + 3 ) / 3 = 6 / 3 = 2 → media aritmetica

1² + 2² + 3² = 1 + 4 + 9 = 14 → suma patratelor celor 3 numere consecutive

2 / 14 = 1 / 7 → raportul dintre media aritmetica si suma patratelor celor 3 numere consecutive